It appears from this records are kept with Maui’ s records
From:
http://www.chem.hawaii.edu/uham/counties.html
Called Kalawao County, Hawaii’s fifth county included the peninsula of Kalaupapa on the north side of the island of Molokai and a portion of the steep cliff face overlooking this area, and perhaps a bit of the land near the top of East end of the cliffs. The district/county lines continue to the east through very rough country and eventually back down to the Pacific.
This area was set aside very early on, in the 1880’s, as a colony for sufferers of Hansen’s Disease, Leprosy. It is where Father Damien (now Blessed Damien) worked. It was created as a county along with the other four Hawaii counties in 1905. It unusual in that it was administered as a separate County by the Department of Health. Thus it has had special status from its creation.
Several decades ago the old county lines became district lines, and this political area was absorbed into Maui county as one of its new judicial districts. An authoritative map published in 1983 already clearly shows the old county lines as district lines and as part of Maui County. So this fifth county does not seem to exist today, at least not in terms of political geography.
Prior to its conversion to a judicial district in Maui county, it was perhaps the rarest county in the United States for county hunters. Population in that area had dwindled to few hundred at most. The area at the top of the cliffs was pasture land. The district line scims along just below the edge of the cliff. Older maps the UHM library map collection show the county clearly and seem to confirm that the older county lines are exactly the same as the modern district lines.